Question

A small village, having a population of 5000, requires 75 litres of water per head per day. The village got an overhead tank of measurement $40m\times 25m\times 15m$. For how many days will the water of this tank last?

Answer 1

Hint: The overhead tank is a cuboidal figure. We find the volume of the tank from the given measurements and convert it into litres. Now, we find the water requirements on a daily basis. At the end we divide the tank volume by daily requirement of water in that village to get the number of days the water of that tank will last.

Complete step-by-step answer:
Every villager of that village needs 75 litres of water per day.
The population of the village is 5000. So, the total requirement of the water in that village on a daily basis is $75\times 5000=375000$ litres.
The water is provided from an overhead tank of measurement $40m\times 25m\times 15m$.
The tank is a figure of cuboid whose volume is required.
So, the volume of the tank is $length\times breadth\times depth$. Here the measurements are $length=40,breadth=25,depth=15$.

Putting the values, we get $40\times 25\times 15=15000{{m}^{3}}$.
We also know that $1{{m}^{3}}=1000litre$. So, converting the volume of the tank into litre form we get $15000{{m}^{3}}=\left( 15000\times 1000 \right)$ litres.
Now we divide it by the daily requirement to get the number of days the water of this tank will last.
We are going to use a unitary method. The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value. In essence, this method is used to find the value of a unit from the value of a multiple, and hence the value of a multiple.
So, the number of days is $\dfrac{\left( 15000\times 1000 \right)}{375000}=\dfrac{15000}{375}=40$.
The water of the overhead tank will last for 40 days.

Note: At the time of solving these kind of mensuration problems we always should be very careful about the units. We always use conversion to get to the same unit form for conducting any kind of operations.